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We introduce a minimal model of energy transfer through scales to describe, at a qualitative level, the subcritical transition between laminar and turbulent flows, viewed in a statistical physics framework as a discontinuous absorbing phase transition. The main control parameter of the model is a Reynolds number that compares energy transfer to viscous dissipation on a large length scale. In spite of its simplicity, the model qualitatively reproduces a number of salient features of the subcritical laminar-turbulent transition, including the existence of an absorbing laminar state, the discontinuous onset of a metastable fluctuating turbulent state above a threshold Reynolds number, and a faster-than-exponential increase of the turbulence lifetime when increasing the Reynolds number. The behavior of the model is also consistent, at high Reynolds number, with the Kolmogorov K41 phenomenology of fully developed turbulence. [ABSTRACT FROM AUTHOR]

The drag crisis in flow past a sphere is modeled within the framework of the recently formulated scale-resolving hybrid RANS−LES approach, which includes a semi-empirical model of laminar-turbulent transition. The calculations performed in a wide Reynolds number range show that the complex model used yields a qualitatively adequate description of all aspects of the drag crisis including such fine effects, as the growth of the side force oscillation amplitude at near-critical Reynolds numbers. At the same time, the results obtained indicate that very fine computation grids should be used for obtaining qualitatively accurate predictions of the critical Reynolds number and the details of laminar-turbulent transition in near-critical flow regimes. [ABSTRACT FROM AUTHOR]

The disturbances generated by external turbulence in the shear layer on a flat plate suddenly set in motion are found. As the initial conditions, turbulent flow found using direct numerical simulation of the development of isotropic homogeneous turbulence is used. The solution obtained models laminar-turbulent transition in the boundary layer on a flat plate under relatively low free-stream turbulence when the transition is caused by Tollmien–Schlichting waves. The solution makes it possible to describe the process of generating various disturbances, namely, low-frequency streaky structures and instability waves and also their development in the initial stage of laminar-turbulent transition. Based on the processing of the obtained results, a simple model is proposed that relates the spectra of instability waves in the boundary layer and turbulent pulsations in free-stream flow. The dependences of the initial amplitude of instability waves and their critical amplification factors (N-factors) on the degree of flow turbulence are also obtained. [ABSTRACT FROM AUTHOR]

This paper presents the results of extensive testing of four recently proposed algebraic laminar-turbulent transition (LTT) models, which are significantly more computationally effective than differential models, while being potentially equally accurate. The models chosen for evaluation, namely, SST KD, SST kγ, SST alg-γ, and SA BCM, are implemented in the in-house code NTS and verified by comparing the obtained results with those published by the models' authors. The experimental database used for the evaluation of the models includes transitional boundary layers at different free-flow turbulence intensities with and without the pressure gradient, four airfoil flows with different LTT scenarios, and a tandem of two airfoils. It is found that at low levels of turbulence, the results of the SA BCM and SST kγ models may depend on the initial approximation, which does not allow them to be recommended for engineering applications. The best results, comparable in accuracy to those of differential models, are obtained using the SST alg-γ model. [ABSTRACT FROM AUTHOR]

Comparative calculations of the location of the onset of the laminar-turbulent transition zone are performed using the eN-method for two points on the Mars "Pathfinder" entry trajectory. A three-component model of thermochemically nonequilibrium CO2–CO–O mixture is used in the calculations. The set of spatial disturbance frequencies is found using neutral curves for the first unstable modes of temporary disturbances. The transition Reynolds number ReδT is determined from the envelopes of families of N-factor curves at NT = 8. In the hypersonic regime at M = 12.6, taking into account the developed thermochemical nonequilibrium leads to a significant decrease in the static temperature of gas in the lower part of the boundary layer. As a result, the onset of the laminar-turbulent transition zone is displaced downstream by approximately 9% as compared to the case of a perfect gas. [ABSTRACT FROM AUTHOR]

Equations describing nonstationary and stationary flows of an incompressible polymer fluid through a pipe are derived based on the rheological mesoscopic Pokrovskii–Vinogradov model. Their exact stationary solutions are obtained and conditions providing their existence are outlined. Numerical simulation of the stabilization of a nonstationary flow is carried out and the restrictions on the values of parameters that ensure stabilization are computed. In a number of cases these restrictions coincide with the conditions of the existence of stationary solutions. The obtained results enable us to describe constructively the process of destruction of laminar Poiseuille-type flows, which usually initiates the onset of turbulence. The key role in mechanics of this process is played by the size and orientation of macromolecules of the polymer fluid. The mathematical description of the process uses essentially the solutions' singular points. [ABSTRACT FROM AUTHOR]

Results of experimental investigations on control of the laminar–turbulent transition location in a 45-degree swept-wing boundary layer by the distributed micro-sized roughness (MSR) elements in presence of freestream perturbations are discussed in this two-part work. Part 1 of this study Borodulin et al. (2023) is devoted to the freestream turbulence effects, while Part 2 (the present paper) concentrates on consideration of the acoustic waves' effects. This paper contains: (i) a complementary description of the experimental setup and measurement techniques related to the acoustic excitation and (ii) the results of studies of the freestream acoustic-field effects on the MSR transition control. The robustness of the MSR transition-control mechanism has been studied by altering the wind-tunnel flow quality: by introducing a significant background sound and/or by simultaneous variation of both the freestream turbulence level and the level of the acoustic wave excitation. At enhanced freestream turbulence, the laminar–turbulent transition is found to move upstream regardless of the sound level and frequency, while the MSR-elements lost their effectiveness in transition control in all cases. At low freestream turbulence levels and in absence of the MSR, the acoustic waves did not affect basically the transition location. However, if the laminar–turbulent transition was delayed by the MSR, the sound of a certain frequency was found to be able to cause a significant additional transition delay. [ABSTRACT FROM AUTHOR]

The creation of hairpin or lambda vortices, typical for the early stages of the laminar-turbulent transition process in various boundary layer flows, in some sense may be associated with blow-up solutions of the Fisher--Kolmogorov--Petrovsky--Piskunov equation. In contrast to the usual applications of this nonlinear evolution equation of the reaction-diffusion type, the solution quantity in the present context needs to stay neither bounded nor positive. We focus on the solution behavior beyond a finite-time point blow-up event, which consists of two moving singularities (representing the cores of the vortex legs) propagating in opposite directions, and their initial motion is determined with the method of matched asymptotic expansions. After resolving subtleties concerning the transition between logarithmic and algebraic expansion terms regarding asymptotic layers, we find that the internal singularity structure resembles a combination of second- and first-order poles in the form of a singular traveling wave with a time-dependent speed imprinted through the characteristics of the preceding blow-up event. [ABSTRACT FROM AUTHOR]

The paper presents the results of an experimental study of the influence of distributed engines mounted downstream of the trailing edge on the structure of a separated flow around a trapezoidal model of a flying wing in a subsonic wind tunnel. Visualization patterns of the near-wall flow on the leeward side of the model are obtained in the modes of blocked engines and for the rotational speed of the impeller of 32800 rpm in the range of angles of attack of the wing . The studies also take into account the location of distributed propulsion relative to the level of the trailing edge, where the axis of rotation of the engine impeller coincided with the continuation of the wing chord line or is higher than that. The possibility of controlling a separated flow by using sources of stationary disturbances in the form of cones and ribs locally mounted at singular points on the wing surface is studied. [ABSTRACT FROM AUTHOR]

This paper touches upon the effect of an amplitude of a deflector introduced into a laminar jet flow on the linear change coefficient of the radial component of a stationary perturbation. Methods for introducing and measuring the perturbations are described. It is shown that a decrease in the deflector amplitude has no effect on the flow pattern, cannot prevent an algebraic growth mechanism, and causes a proportional decrease in the radial component of the stationary velocity perturbation. Turbulence is established after reaching some radial expansion value that is independent of the initial perturbation amplitude. [ABSTRACT FROM AUTHOR]

Under the low-noise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminar-turbulent transition is due to amplification of the first mode. Stability of a local self-similar boundary layer over such a wing is investigated both using the e N method in the framework of linear stability theory and direct numerical simulation (DNS). It is found that the instability amplitude should reach a maximum over the entire spectral range above the profiles of 2.5% and thicker. The locus of maximum appears at the trailing edge and moves to the leading edge as the profile becomes thicker, while the maximum amplitude decreases. The theoretical findings are supported by DNS of the linear wave packets propagating in the boundary layer. Significance of these results to the design of laminar supersonic wings is discussed. [ABSTRACT FROM AUTHOR]

A computational methodology is presented for calculating the spatial evolution of Tollmien–Schlichting (T–S) waves and their amplitude growth-rate factor in substantially nonparallel compressible flows, based on a global stability analysis of stationary solutions of the full Navier–Stokes (N–S) equations. Three stages of this methodology (obtaining a stationary solution, as well as carrying out a global stability analysis and its postprocessing) are described, and the results are presented of its validation based on the comparison of the results of calculating the characteristics of T–S waves on a flat plate with the corresponding results of the classical stability theory in the parallel approximation. An example of calculating the flow around a plate with a rectangular cavity is presented to illustrate the possibility of applying the proposed methodology to nonparallel flows. [ABSTRACT FROM AUTHOR]

Results of experimental investigations on control of the laminar–turbulent transition location in a 45-degree swept-wing boundary layer by the distributed micro-sized roughness (MSR) elements in presence of freestream perturbations are discussed in this two-part work. Part 1 of this study (the present paper) is devoted to the freestream turbulence effects, while Part 2 (Borodulin et al., 2023) concentrates on consideration of the acoustic waves' effects. The present paper (Part 1) contains: (i) a brief description of previous studies in the field, (ii) description of the experimental setup and techniques of the measurements (based on infrared thermography), (iii) the results of optimization of parameters of the MSR-elements, and (iv) results of studies of freestream turbulence effects on the MSR transition control. The MSR-elements are shown to excite in the boundary layer controlled stationary vortices, which are able to modify significantly both the base flow and its stability characteristics. Variation of the height and the period of the MSR-elements allowed us to find the most stabilizing effect on the boundary layer flow compared to the case without MSR as a reference one. A significant downstream shift in the position of the laminar–turbulent transition caused by the MSR has been detected and documented in detail. The robustness of this flow control method to freestream turbulence has been studied by increasing the turbulence level by means of turbulence generating grids. At enhanced freestream turbulence levels, the laminar–turbulent transition was found to move upstream, while the MSR-elements lost their effectiveness in the transition control. [ABSTRACT FROM AUTHOR]

The use of modern computer systems for calculating the aerophysical characteristics of supersonic bodies of revolution together with the calculation of the flight trajectory under conditions of continuously changing Mach and Reynolds numbers of the oncoming flow, the presence of transient regimes and non-isothermality in near-wall flows is often not possible due to the complexity of the organisation of the computational process. By using a number of integral methods for calculating inviscid flows and viscous compressible near-wall flows, talcing into account the non isothermality and intermittency of the boundary layer, a method has been developed for calculating the friction and heating of supersonic bodies of revolution on the flight trajectory. On the basis of well-known flight experiments, the correlation dependences of the Reynolds numbers of the beginning of the transition on sharp cones were obtained and the method of corrections for spherical blunting of the head part was implemented. By calculating the intermittency function, the changeability of flow regimes in the boundary layer is established for a number of trajectories of the supersonic uncontrolled rocket projectile. Calculated dependences for aerodynamic friction, heat fluxes and projectile wall temperature on the flight time are obtained. The concept of combined calculation of aerophysical characteristics on the flight trajectory using numerical and integral methods is proposed. [ABSTRACT FROM AUTHOR]

In a model experiment, the process of interaction of an external artificial disturbance with the leading edge of a straight wing model was investigated. The characteristics and features of the development of boundary layer disturbances, generated as a result of the interaction of external disturbances, and the blunted leading edge of the wing model have been obtained. The research was carried out in a subsonic low-turbulence wind tunnel using a hot-wire anemometry method for detecting disturbances. Localized disturbances generated in the incoming flow were shown to induce longitudinal streaky structures in the boundary layer of the straight wing. High-frequency wave packets (precursors) appeared at the boundaries (fronts) of longitudinal structures. The dynamics of the development of wave packets and localized longitudinal structures in the boundary layer above the wing profile in a gradient flow was studied. [ABSTRACT FROM AUTHOR]

Approximations of the profiles of the longitudinal and transverse velocity components in the boundary layer calculated for the flows around a swept wing and a body of revolution by means of solving the full Navier–Stokes equations and using the boundary layer profiles from the self-similar one-parameter family of the Falkner–Skan–Cooke profiles and two-parameter family of profiles proposed by Gaster are compared. A significant advantage of using the approximation of the numerical profiles near three-dimensional separation by profiles from the two-parameter family is demonstrated. [ABSTRACT FROM AUTHOR]

The full Navier–Stokes equations are used to study the linear stability of plane Poiseuille flow in a channel with the lower wall corrugated along the flow, due to which the flow has two velocity components. A generalized eigenvalue problem is solved numerically. Three types of perturbations are considered: plane periodic (zero Floquet parameter), plane doubly periodic (finite values of the Floquet parameter), and spatial perturbations. Neutral curves are analyzed in a wide range of the corrugation parameter and Reynolds number. It is found that the critical Reynolds number above which time-growing perturbations appear depends in a complex way on the dimensionless amplitude and period of corrugation. It is shown that in the case of flow in a channel with corrugated wall, three-dimensional perturbations are usually more dangerous. The exception is the small amplitude of corrugation at which plane perturbations are more dangerous. [ABSTRACT FROM AUTHOR]

This study investigates a re-entry scenario of an Apollo-like space capsule with Direct Numerical Simulations (DNS). The simulation includes the chemical equilibrium gas model. Cross-flow-like vortices are induced through random distributed roughness patches on the capsule surface. Two different machine learning methods are used to predict the maximum vorticity magnitude downstream of a pseudo-random roughness patch, the wall-normal location of the vortex core and spanwise and wall-normal gradient maxima of u. A large DNS database is formed for training and testing of the neural networks. In order to understand the influence of the vorticity magnitude on the transition process, local one-dimensional inviscid (LODI) relations are used to describe perturbations at the inflow. The disturbance evolution in the streamwise direction is analysed with a two-dimensional Fourier transformation in time and space. We show how the vorticity magnitudes of the cross-flow-like vortices, spanwise and wall-normal derivatives of the streamwise velocity influence the transition location. [ABSTRACT FROM AUTHOR]

The linear stability of plane Poiseuille flow in a channel with the corrugated bottom wall is considered using the full Navier–Stokes equations. The wall is corrugated across the flow, and main flow has a single velocity component. The perturbations of the velocity and pressure fields are three-dimensional and have two wavenumbers. The generalized eigenvalue problem is solved numerically. It is found that the critical Reynolds number, above which perturbations grow with time, depends on the dimensionless amplitude and the corrugation period in a complex way. The corrugation amplitude/period ratio separates the dimensionless corrugation amplitude into two regions in which the dependences of the critical Reynolds number on the corrugation parameters are qualitatively different. [ABSTRACT FROM AUTHOR]

The analysis of bifurcations and chaotic dynamics for nonlinear systems of a large size is a difficult problem. Analytical and numerical approaches must be used to deal with this problem. Numerical methods include solving some of the hardest problems in computational mathematics, which include system spectral and algebraic problems, specific nonlinear numerical methods, and computational implementation on parallel architectures. The software structure that is required to perform numerical bifurcation analysis for large-scale systems was considered in the paper. The software structure, specific features that are used for successful bifurcation analysis, globalization strategies, stabilization, and high-precision implementations are discussed. We considered the bifurcation analysis in the initial boundary value problem for a system of partial differential equations that describes the dynamics of incompressible ABC flow (3D Navier–Stokes equations). The initial stationary solution is characterized by the stability and connectivity to the main solutions branches. Periodic solutions were considered in view of instability transition problems. Finally, some questions of higher dimensional attractors and chaotic regimes are discussed. [ABSTRACT FROM AUTHOR]

Activities aimed at studying stabilization of a high-speed boundary layer with the use of porous coatings are reviewed. All types of coatings used in experimental research are considered. It is demonstrated that a porous coating with optimal parameters can stabilize the second mode of disturbances to a large extent and delay the laminar–turbulent transition in a high-speed boundary layer. A review of numerical investigations of porous coatings is presented, and it is shown that special boundary conditions are imposed for porous coating modeling; otherwise, the flow has to be calculated in each pore of the coating. The major part of results obtained on the basis of the linear stability theory and in direct numerical simulations agree well with experimental data. Examples of methods of porous coating optimization and of using promising metamaterials are provided. [ABSTRACT FROM AUTHOR]

An investigation of flow acceleration from initial statistically steady turbulent flow to final statistically steady turbulent flow is conducted experimentally using particle image velocimetry (PIV) and constant temperature anemometry (CTA). The turbulence response is investigated as the acceleration periods and acceleration rates are varied in a controlled fashion. This work expands the research by Mathur et al. (2018, "Temporal Acceleration of a Turbulent Channel Flow," J. Fluid Mech., 835, pp. 471-490.) studying slower and longer transient flows. It also complements the numerical studies of a step increase in the flowrate of (He and Seddighi, 2013, "Turbulence in Transient Channel Flow," J. Fluid Mech., 715, pp. 60-102. and He and Seddighi, 2015, "Transition of Transient Channel Flow After a Change in Reynolds Number," J. Fluid Mech., 764, pp. 395-427.). The results obtained from the current investigations are qualitatively similar to those obtained previously. Consistent with previous studies, the response of turbulence in the current slow transient flow is again characterized by a laminar-turbulent transition. The initial increase of the flow development among the cases investigated can be categorized as faster, medium, and slower responses. Modifications are made to the equivalent Reynolds number and the initial turbulence intensity proposed earlier in order to account for the slow accelerating flow rates and the continuous change of the bulk velocities of the cases investigated. It has been shown that the critical equivalent Reynolds number based on these modifications and the initial turbulence intensity are well correlated for all cases investigated and a power-law relation is established. [ABSTRACT FROM AUTHOR]

The influence of the selected mathematical model in simulation of the compressor flow passage of the microturbine engine, is studied. The significant influence of the turbulent model on the character of gas flow in compressor, its compression ratio and efficiency, is shown. [ABSTRACT FROM AUTHOR]

The Navier-Stokes equations describing the motion of viscous/real fluids in Rn (n = 2 or 3) depend on a positive coefficient (the viscosity, ν) via the Reynolds number. The key of NSE problem is the Reynolds number, mathematically considered a simple small perturbation parameter without any physical explanation, or a vague physical Newtonian ratio of inertial to viscous forces, 𝑅𝑅𝑅𝑅=𝑈𝑈𝑈𝑈𝜈𝜈, in spite of its quantic physical meaning as the initial excitation to response ratio, at the beginning of motion (IC at t = 0). The paper deals with the thixotropic property of real viscosity which softens (ν ↓) when strained (Re↑), but it doesn’t tend to zero (ν → 0) as much as the Reynolds number increases, holding a finite value, corresponding to the new thermodynamic equilibrium state. The (ν → 0 for Re → ∞) false physical condition renders the NSE problem to a unique solution less one beyond a critical Reynolds number, Recr. The understanding of the wall-bounded viscous flows, at both small-scales (slow motion, small Re) and larger scale (turbulent motion, large Re) must be in conjunction with the more-subtle torsional buckling effect of the “wall” lag concept that the wall has on the inherent fluid dynamics during the starting phase. The limitations of the diathermal wall associated with the starting accelerations at the onset of motion, of the order of acr/g ≥ 2/3, create the physical conditions (thermomolecular changes) for the loss of the mathematical uniqueness of the NSE solutions. The physical limitations in conjunction with the validity area of NSE model are considered in the sequel. Because of the nonlinearity of the PDE differential equations, the variation of geometrical and physical properties can lead to bifurcations in the solution and thus, to multiple solutions. Considerations relative to laminar-turbulent transition as the main bifurcation source for the more complex structure of a solution, engendered by molecular structure changes of a flowing fluid in more or less contact with the walls, are given and illustrated for the canonical flows on flat plates and viscous decay of a starting/contact vortex (“vortex eye”).

The results of calculations of the convective heating of a sharp plate placed in a supersonic flow at a speed of M = 6–8 are presented. The NERAT-2D code is used for calculations, which implements the Reynolds-averaged Navier−Stokes equations, together with Baldwin–Lomax and Prandtl algebraic models of turbulence. Good agreement is shown with the experimental data for convective heating in a turbulent boundary layer. The distribution of gas-dynamic functions is analyzed in different cross sections of the plate within the flow. [ABSTRACT FROM AUTHOR]

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability. [ABSTRACT FROM AUTHOR]

Cancellation of the cross-flow vortices in a swept-wing boundary layer is attempted by plasma actuator array in numerical simulation. The response of the boundary layer to the stationary excitation by a single actuator section is measured experimentally and compared to the response obtained from the solution to the parabolized stability equations. A linear approach is shown to be held within the peak-to-peak magnitude of the stationary cross-flow vortices below 10% of the local potential flow velocity. Within the linear model, an optimal control strategy and a faster suboptimal one are developed to calculate voltage amplitude distribution across the electrodes, taking into account the forcing constraints. Simulation of the cancellation process is performed, showing up to a 20 dB reduction in the initial spanwise velocity modulation in the boundary layer. The minimal actuator resolution required for the successive implementation of the control is shown to be in the order of a quarter of the most amplified wavelength, or 3–4 displacement thickness of the boundary layer. Linear estimates predict up to a 150 mm (22% of flow acceleration region length) transition delay for an actuator momentum coefficient of 0.005%. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of direct numerical modeling of the process of susceptibility of a supersonic boundary layer over an unswept wing with a thin parabolic profile to acoustic noise of various intensities. It was demonstrated that acoustic noise can cause a laminar–turbulent transition over the unswept wing of a supersonic passenger aircraft. [ABSTRACT FROM AUTHOR]

An optimal two-row six-blade X-propeller is compared with a conventional three-blade and six-blade propeller mounted in the same rings. [ABSTRACT FROM AUTHOR]

It is known that, in wall-bounded flows, along with the growth of instability modes, an important role is played by the nonmodal (algebraic) mechanism of linear growth. In unbounded flows, including submerged jets, the nonmodal growth mechanism has been theoretically studied only in the last decade; this mechanism has not yet been identified in experiments. This paper describes experiments on excitation of the nonmodal "lift-up" growth mechanism. Special wavy structures (deflectors) are introduced into a laminar submerged jet of circular cross section, which excites a roller-like transverse motion. The data obtained make it possible to identify unambiguously the nonmodal lift-up growth of the introduced perturbations. The development of perturbations in the experiment qualitatively agrees with the theoretically calculated optimal perturbations. The specificities of the transition to turbulence caused by nonmodal growth are considered. [ABSTRACT FROM AUTHOR]

The heating of oil and oil products is widely used to reduce energy losses during transportation. An approach is developed to determine the effective length of the heat exchanger and the temperature of the cold coolant (oil) at its outlet in the case of a strong dependence of oil viscosity on temperature. Oil from the Uzen field (Kazakhstan) is considered as a heated coolant, and water is considered as a heating component. The method of the log–mean temperature difference, modified for the case of variable viscosity, and the methods of computational fluid dynamics (CFD) are used for calculations. The results of the numerical calculations are compared with the data obtained on the basis of a theoretical approach at a constant viscosity. When using a theoretical approach with a constant or variable viscosity, the heat transfer coefficients to cold and hot coolants are found using criterion dependencies. The Reynolds-averaged Navier–Stokes (RANS) and a turbulence model that takes into account the laminar–turbulent transition are applied. In the case of variable oil viscosity, a transition from the laminar flow regime to the turbulent one is manifested, which has a significant effect on the effective length of the heat exchanger. The obtained results of the CFD calculations are of interest for the design of heat exchangers of a new type, for example, helicoid ones. [ABSTRACT FROM AUTHOR]

This work is devoted to a numerical study of the influence of foreign-gas injection on the stability of compressible boundary layer on a concave surface. The stability calculation was carried out within the framework of the locally parallel linear stability theory. The results of calculations for the reference case without injection showed that Görtler vortices and the second Mack mode exhibited the highest growth rates at studied parameters. It is found that the injection of a heavy gas (with respect to the oncoming gas) leads to an increase in the growth rate of Görtler vortices and the second Mack mode, whereas the injection of a light gas leads to a decreased growth rate of these disturbances. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of the evolution of turbulent spots in the boundary layer on a flat plate at a zero angle of attack at the freestream Mach number M∞ = 6 are carried out. The propagation of artificially excited localized three-dimensional vortical disturbances with different initial amplitudes, which, when propagating downstream, develop into turbulent spots, is considered. A direct numerical simulation is performed by solving the Navier–Stokes equations for three-dimensional compressible gas flows using the in-house solver that implements an implicit shock capturing numerical scheme. It is shown that the universal quasi-monotonic numerical scheme makes it possible to correctly estimate the main characteristics of turbulent spots: the transverse spreading angle and the velocities of the leading and trailing fronts. The agreement between the parameters of the obtained spots and the results of other authors is demonstrated. [ABSTRACT FROM AUTHOR]

The use of small rotors has increased due their applications in drones and UAVs. In order to improve the global performance of these aerial vehicles, it is necessary to understand the aerodynamics of small rotors, since this is related to the global energy consumption of such vehicles. Most of the computational fluid dynamics (CFD) studies found in the literature that are related to the analysis of small rotors employ fully turbulent models, despite the low-to-moderate Reynolds numbers of these applications. This paper presents CFD simulations for a small rotor at hover at different Reynolds numbers using fully turbulent and transitional SST k − ω turbulence models. Numerical results show that thrust and torque are close to experimental measurements, showing differences of less than 5% for both fully turbulent and transitional models. However, significant differences were observed between the fully turbulent and the transitional models when studying the boundary-layer development and separation. As the Reynolds number was increased, it was observed that at the tip of the blade, these differences were reduced, but at mid-span, the differences were more obvious. [ABSTRACT FROM AUTHOR]

The most promising areas of research in the field of plasma aerodynamics are proposed. On the basis of the presented experimental data obtained recently, the possibilities of using the volumetric force effect on the gas flow in aerodynamic applications, which is realized with the help of near-surface electric discharges, are considered. One of these applications is to increase the length of the laminar section of the boundary layer on the swept wing in order to reduce the aerodynamic drag of the aircraft in the cruise flight mode. The second direction is associated with the control of the three-dimensional separation of the boundary layer on the elements of the mechanization of the swept wing in the take-off and landing modes. The third direction is the reduction of surface friction in the turbulent boundary layer, which is realized on most of the surface of modern near- and supersonic aircraft. The proposed studies are not only of applied, but also of fundamental importance due to the physical complexity of the studied phenomena. [ABSTRACT FROM AUTHOR]

The Navier-Stokes equations describing the motion of viscous/real fluids in Rn (n = 2 or 3) depend on a positive coefficient (the viscosity, v) via the Reynolds number. The key of NSE problem is the Reynolds number, mathematically considered a simple small perturbation parameter without any physical explanation, or a vague physical Newtonian ratio of inertial to viscous forces, RRRR = UUUU vv, in spite of its quantic physical meaning as the initial excitation to response ratio, at the beginning of motion (IC at t = 0). The paper deals with the thixotropic property of real viscosity which softens (v ↓) when strained (Re↑), but it doesn't tend to zero (v → 0) as much as the Reynolds number increases, holding a finite value, corresponding to the new thermodynamic equilibrium state. The (v → 0 for Re → ∞) false physical condition renders the NSE problem to a unique solution less one beyond a critical Reynolds number, Recr. The understanding of the wall-bounded viscous flows, at both smallscales (slow motion, small Re) and larger scale (turbulent motion, large Re) must be in conjunction with the more-subtle torsional buckling effect of the "wall" lag concept that the wall has on the inherent fluid dynamics during the starting phase. The limitations of the diathermal wall associated with the starting accelerations at the onset of motion, of the order of acr/g ≥ 2/3, create the physical conditions (thermomolecular changes) for the loss of the mathematical uniqueness of the NSE solutions. The physical limitations in conjunction with the validity area of NSE model are considered in the sequel. Because of the nonlinearity of the PDE differential equations, the variation of geometrical and physical properties can lead to bifurcations in the solution and thus, to multiple solutions. Considerations relative to laminarturbulent transition as the main bifurcation source for the more complex structure of a solution, engendered by molecular structure changes of a flowing fluid in more or less contact with the walls, are given and illustrated for the canonical flows on flat plates and viscous decay of a starting/contact vortex ("vortex eye"). [ABSTRACT FROM AUTHOR]

The generation and development of Görtler vortices in compressible boundary layer on a concave surface has been numerically simulated. The calculation was carried out using the Ansys Fluent software. Stationary and non-stationary disturbances are analyzed at freestream Mach number M ≈ 4. It is shown that when a periodic disturbance in the direction transversal to the flow is generated, it decays on the straight section of the surface, and grows on the concave surface. Comparison of the results of the calculations made with the calculations performed within the framework of the linear stability theory showed that the range of receptivity of the boundary layer to the disturbances on the concave surface amounts approximately to 17 boundary-layer thicknesses. After the receptivity zone, disturbances grow exponentially with small deviations. The flow fluctuation profiles are in good agreement with the data obtained from the linear stability theory. It is shown that the development of a non-stationary disturbance along the surface of the model for the parameters considered in the present study differs little from that of a stationary disturbance. [ABSTRACT FROM AUTHOR]

On the basis of stochastic differential equations of conservation laws and the theory of equivalence of measures, the dependence is obtained for the coefficient of hydraulic friction in a smooth round pipe for a laminar–turbulent flow of an incompressible fluid depending on the intensity of turbulence, the scale of turbulence, the index of the velocity profile, and the Reynolds number. All the listed parameters included in the final formula of hydraulic friction are also determined by the corresponding formulas based on stochastic equations for the Reynolds number in a laminar–turbulent flow regime. In carrying out the calculations, the parameters of the initial disturbances are determined from known experimental data on the initial turbulence in a flow through a smooth round pipe. It is shown that, by applying a new dependence for the laminar–turbulent regime, which takes into account the parameters of the initial disturbance in the flow of deterministic motion, the dependence for the friction coefficient can be determined, which is obtained for a fully developed turbulent flow on the basis of stochastic equations. The friction coefficient for flow through a smooth pipe in a laminar–turbulent regime is calculated in the Reynolds number range from 2300 to 4500 and includes the fully developed turbulent flow regime in the Reynolds number range of 4500–7000. The obtained results of the values of the coefficient of friction show both quantitative and qualitative agreement with the known experimental data of Nikuradze. It is important to emphasize that, applying the dependence of the friction coefficient derived in the study for the laminar–turbulent flow through a smooth circular tube, it is possible to explain the differences between the values of the experimental results both for the laminar–turbulent regime and for the fully developed turbulent flow in a tube with the same Reynolds number, which can be caused by different values of the initially existing flow pulsations in each specific experiment. Results which are presented in article probably open up prospects both for the development of new experimental measuring instruments and for the development of a new calculation method—direct theoretical–numerical simulation (DTNS). [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical simulation for the development of localized disturbances emerging from a single source or two synchronous sources of laminar boundary disturbances allocated on the plate with the flow at Mach number M = 2 (variants for different distances between two sources were considered). Simulation was performed using the FlowVision software package at the flow parameters typical of T-325 wind tunnel (ITAM SB RAS). The problem was studied in the range of the linear development of disturbance. The study demonstrates that, depending on the distance between the sources, the generated disturbances might either enhance or decay downstream. The frequency-wave analysis of disturbance structure was performed. Two separated synchronous local sources generate the disturbances with wave spectra: these spectra exhibit nodes and antinodes and their positions depend on the distances between two sources. [ABSTRACT FROM AUTHOR]

A new algebraic RANS model for laminar–turbulent transition will be presented. The model follows the Local-Correlation-based Transition Modeling concept, is Galilean invariant and can handle natural, bypass and separation-induced transition. The model formulation is discussed in detail. A substantial number of test cases have been computed to evaluate the different transition mechanisms of the model. [ABSTRACT FROM AUTHOR]